On massive spin 2 electromagnetic interactions

TL;DR

The paper addresses electromagnetic interactions of a massive spin-2 particle in $(A)dS$ backgrounds within a gauge-invariant framework. It employs a bottom-up approach, starting from minimal EM coupling and adding non-minimal, higher-derivative vertices (up to three derivatives) with corresponding gauge transformation corrections, in both metric-like and frame-like formalisms. A central result is a non-singular relationship between the electric charge, mass, and cosmological term, $e_0 = - a_0 [ m^2 - \kappa(d-2) ] \frac{d-3}{d-2}$, with a parallel expression in the frame-like formalism, and a partially massless point at $m^2 = \kappa(d-2)$ where a scalar sector decouples. The constructions yield a model that smoothly interpolates between a massless spin-2 in $(A)dS$ and a massive one in flat space, while preserving the correct degrees of freedom and suggesting a generalization to higher spins and non-linear regimes.

Abstract

In this paper we investigate electromagnetic interactions for massive spin 2 particles in (A)dS space at linear approximation using gauge invariant description for such massive particles. We follow bottom-up approach, i.e. we begin with the introduction of minimal interaction and then proceed by adding non-minimal interactions with higher and higher number of derivatives together with corresponding non-minimal corrections to gauge transformations until we are able to restore gauge invariance broken by transition to gauge covariant derivatives. We manage to construct a model that smoothly interpolates between massless particle in (A)dS space and massive one in a flat Minkowski space. Also we reproduce the same results in a frame-like formalism which can be more suitable for generalizations on higher spins.